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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 215, page id 826603459:0261
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CAP. 24.
De Geodaesia.
de cau (a) ex ductu ejuldem aliicudinis BF in ZF C semissem
basis Cuxe; Horum icaq. criengulorum ditferencia, quod est ip.
cum criangulum BCB expolicum, est = E B + BF = Z P C. XBF,
quod cancundem estacqi ZFB = = FC (hoc cA = C B) in BF.
(NaM E B in F. C = C B,ideoque ZFB= =FC = = C B, vel
EB = RC
2. D Itagi _ HOC PAEIO CMEr∞EE area XQULA.
EEB = =EC = = CB
XBF
EEBABE L ZF C ABE = =CBXBF
lis semisi alcicudinis in basin duerae.
Scd _ idem alicer ostenditur; (ACq; cadem opera, non mon.
do Triangulum rectangulum, quod modo dictum est, (cd e
Trianculum quodvis rectilineum esse Paralleloerammi dimidium.) Si
Triangulum expolicum BCB. ( Pire Rectangulum, sive acutan.
gulum, Eire obcutangulum) super basi BB consticurum (ica
nempeut perpendicularis a verrice cadar inera Triangulum)
inscribatur Parallelogrammo Rectangulo super eadem bale,
eandem icem alcicudinem habenei cum ipso criansulo, nempe
DB. Cum enim criangula rectangula C AB, C. AB, sinc sigilla-
eim aequalia lemissibus parallelogrammorum AD, AN; erie de
aegreparum illorum, hoc est, Triangulum eC B, Cemissi eorius
DB Paralleloerammi (ex duobus AI, As, 28BreBaTI) X-
quale.
Sin extra criangulum cadac perpendicularis (quod in crian-
sulo Obculangulo teri posse diximus) illud idem ostenditur
hoc pacto. Compleco parallelogrammo eCBy (ductis nem-
De B7, B7. laceribus crianguli BC, BC, Parallelis) erune duo
criangula BCA, B76, inricem limilia e aequalia, et Propterea
ucrumris, parallelogrammi Pemislis: Ac parallelogranmum
illud aequacur rectangulo, alcicudine BF vel zB, _ baHC Bvet
B7, comprehento (uc supra osensum eMt) ergo Triangulum
ejuldem Cemissi rguatUE: nempe Temilli quarticatis FactX ex
ductu basis C B in alcicudinem BF, vel quancitati FaCtX eX
ductu lemissis balis in eocam alcicudinem; vel Pemistis alcicudinis
neoram balin; quae omnia cancundem valene; quirre
CB